Why doesn't the wolf eat Little Red Riding Hood when he first encounters her?
In the tale of "Little Red Riding Hood" as told by Perrault and the Grimm brothers, the wolf leaves the little girl and goes to her grandmother's house, where he eats the old lady and then gets in her bed to wait for Little Red Riding Hood to arrive. Why doesn't he eat the little girl first?
There are a good number of collected texts on the Red Riding Hood fable. Taking, for example, the Germany/Poland version as told in Lower Lusatia, (1) Red is not afraid of the Wolf because she has not been schooled in what a wicked animal a wolf can be and (2) the Wolf plotted to intentionally eat both Red and the grandmother:
"She will taste better than the old woman; but you must trick her cleverly, that you may catch both."
The Perrault version actually gives a very sound reason for why he didn't eat her upon first meeting her (here she also does not know Wolves wickedness and so is not afraid): His instinct for self-preservation prevents him since there are woodcutters working nearby:
"[She] met with a wolf, who had a very great mind to eat her up, but he dared not, because of some woodcutters working nearby in the forest ..."
The Grimm version presents the least logical explanation of these three examples. All the Wolf says to himself (for this must be a very dull Wolf) is, hmmm, how shall I catch her?
"Now there is a tasty bite for me. Just how are you going to catch her?"
As a final note, the Marelles version accords with Perrault's and blames the Wolf's lost chance on self-preservation and nearby woodcutters (although this Wolf is a much more evil-minded wolf who lays in wait at the "turn of the road under the trees"):
He had seen the child start alone, and the villain was waiting to devour her; when at the same moment he perceived some woodcutters who might observe him, and he changed his mind.
So though the various versions of this story found across Europe has reasons that vary in degree of logic, cleverness, and viciousness, they do give a reason for the Wolf's hesitation thus for the plan developing around the grandmother.
Neither the version of "Little Red Riding Hood" by Perrault nor the one by the Grimm brothers gives any reason why the wolf does not eat the little girl when he first meets her. The Perrault version was adopted from a much older folk tale, and the Grimm brothers version was adopted from Perrault. The old folk tale may have explained why the wolf acted as he did.
The most likely reason would have been that the wolf lived in a forest which was undoubtedly frequented by hunters, wood choppers, and other men who would kill a wolf on sight. If the wolf had tried to kill and eat Little Red Riding Hood out in the open, she would have screamed and perhaps attracted help. (This is what actually happened inside the grandmother's cottage, at least in some versions of the tale.) So the cunning wolf planned to eat both the grandmother and the little girl inside the cottage, and the only way to do that would be to eat Grandma first and then wait for Little Red Riding Hood to arrive.